Subgroups — C₁₃₉×#21261 #48015857

Order 35584.

1694 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#423×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#419×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	C₂×#418×C₁₃₉	C₂	1	2	yes	maximal
5	C₄×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1983×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
10	C₂×#124×C₁₃₉	—	2	1	no	—
11	C₂×#124×C₁₃₉	—	2	1	no	—
12	C₂×#124×C₁₃₉	—	2	4	no	—
13	C₂×#124×C₁₃₉	C₄	1	8	yes	complemented
14	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
15	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
17	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
18	#423×C₁₃₉	—	2	4	no	—
19	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	4	yes	complemented
20	#419×C₁₃₉	—	2	8	no	—
21	#418×C₁₃₉	—	2	8	no	—
22	C₂×#103×C₁₃₉	C₂²	1	8	yes	complemented
23	C₂×#102×C₁₃₉	C₂²	1	8	yes	—
24	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
25	C₄×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
26	#376×C₁₃₉	—	2	1	no	—
27	C₄³×C₁₃₉	—	2	1	no	—
28	C₂⁵×C₁₃₉	—	2	1	no	—
29	C₂²×Q₈×C₁₃₉	—	2	2	no	—
30	C₂²×Q₈×C₁₃₉	—	2	1	no	—
31	C₂²×Q₈×C₁₃₉	—	2	4	no	—
32	C₂²×Q₈×C₁₃₉	—	2	4	no	—
33	C₂²×Q₈×C₁₃₉	C₂×C₄	1	4	yes	—
34	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
35	C₂²×D₄×C₁₃₉	—	2	4	no	—
36	C₂²×D₄×C₁₃₉	—	2	1	no	—
37	C₂²×D₄×C₁₃₉	—	2	2	no	—
38	C₂²×D₄×C₁₃₉	—	2	4	no	—
39	C₂²×D₄×C₁₃₉	C₂×C₄	1	4	yes	—
40	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₃₉	—	2	1	no	—
42	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
43	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₁₃₉	—	2	4	no	—
45	C₂×M₁₆×C₁₃₉	—	2	4	no	—
46	C₂×M₁₆×C₁₃₉	—	2	4	no	—
47	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
48	#124×C₁₃₉	—	2	8	no	—
49	#124×C₁₃₉	—	2	8	no	—
50	#124×C₁₃₉	—	2	8	no	—
51	#124×C₁₃₉	C₂×C₄	1	16	yes	—
52	#117×C₁₃₉	—	2	4	no	—
53	#117×C₁₃₉	D₄	1	8	yes	—
54	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
55	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
57	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
59	C₂×C₄²×C₁₃₉	—	2	2	no	—
60	C₂×C₄²×C₁₃₉	—	2	4	no	—
61	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
65	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
66	C₄⋊C₈×C₁₃₉	—	2	8	no	—
67	#103×C₁₃₉	—	2	16	no	—
68	#102×C₁₃₉	—	2	16	no	—
69	#95×C₁₃₉	—	2	4	no	—
70	C₂⁴×C₁₃₉	—	2	4	no	—
71	C₂⁴×C₁₃₉	—	2	2	no	—
72	C₂⁴×C₁₃₉	—	4	8	no	—
73	C₂⁴×C₁₃₉	—	4	4	no	—
74	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
75	C₂×Q₈×C₁₃₉	—	2	4	no	—
76	C₂×Q₈×C₁₃₉	—	2	2	no	—
77	C₂×Q₈×C₁₃₉	—	2	16	no	—
78	C₂×Q₈×C₁₃₉	—	2	4	no	—
79	C₂×Q₈×C₁₃₉	—	2	4	no	—
80	C₂×Q₈×C₁₃₉	—	4	4	no	—
81	C₂×Q₈×C₁₃₉	—	4	4	no	—
82	C₂×Q₈×C₁₃₉	—	4	4	no	—
83	C₂×Q₈×C₁₃₉	C₂²×C₄	1	4	yes	—
84	C₂×D₄×C₁₃₉	—	2	4	no	—
85	C₂×D₄×C₁₃₉	—	2	16	no	—
86	C₂×D₄×C₁₃₉	—	2	4	no	—
87	C₂×D₄×C₁₃₉	—	2	2	no	—
88	C₂×D₄×C₁₃₉	—	2	4	no	—
89	C₂×D₄×C₁₃₉	—	4	4	no	—
90	C₂×D₄×C₁₃₉	—	4	4	no	—
91	C₂×D₄×C₁₃₉	—	4	4	no	—
92	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₁₃₉	—	2	4	no	—
94	C₂²×C₄×C₁₃₉	—	2	4	no	—
95	C₂²×C₄×C₁₃₉	—	2	2	no	—
96	C₂²×C₄×C₁₃₉	—	4	4	no	—
97	C₂²×C₄×C₁₃₉	—	4	4	no	—
98	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	8	yes	—
99	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
106	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
107	M₁₆×C₁₃₉	—	4	8	no	—
108	C₂×C₈×C₁₃₉	—	2	4	no	—
109	C₂×C₈×C₁₃₉	—	2	4	no	—
110	C₂×C₈×C₁₃₉	—	2	4	no	—
111	C₄⋊C₄×C₁₃₉	—	2	4	no	—
112	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
113	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
114	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
115	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
116	C₄²×C₁₃₉	—	2	8	no	—
117	C₄²×C₁₃₉	—	4	8	no	—
118	C₄²×C₁₃₉	C₂²⋊C₄	1	4	yes	—
119	C₄²×C₁₃₉	C₂²⋊C₄	1	4	yes	—
120	C₄²×C₁₃₉	C₂²×C₄	1	4	yes	—
121	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
122	C₂³×C₁₃₉	—	2	4	no	—
123	C₂³×C₁₃₉	—	2	4	no	—
124	C₂³×C₁₃₉	—	4	16	no	—
125	C₂³×C₁₃₉	—	4	4	no	—
126	C₂³×C₁₃₉	—	4	8	no	—
127	C₂³×C₁₃₉	—	4	8	no	—
128	C₂³×C₁₃₉	—	8	16	no	—
129	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
130	C₂³×C₁₃₉	#121	1	4	yes	—
131	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₁₃₉	—	2	8	no	—
133	Q₈×C₁₃₉	—	4	2	no	—
134	Q₈×C₁₃₉	—	4	2	no	—
135	Q₈×C₁₃₉	—	4	8	no	—
136	D₄×C₁₃₉	—	2	8	no	—
137	D₄×C₁₃₉	—	4	2	no	—
138	D₄×C₁₃₉	—	4	2	no	—
139	D₄×C₁₃₉	—	4	8	no	—
140	C₂×C₄×C₁₃₉	—	2	4	no	—
141	C₂×C₄×C₁₃₉	—	2	4	no	—
142	C₂×C₄×C₁₃₉	—	2	4	no	—
143	C₂×C₄×C₁₃₉	—	2	8	no	—
144	C₂×C₄×C₁₃₉	—	4	8	no	—
145	C₂×C₄×C₁₃₉	—	4	4	no	—
146	C₂×C₄×C₁₃₉	—	4	8	no	—
147	C₂×C₄×C₁₃₉	—	4	8	no	—
148	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
149	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	4	yes	—
150	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₁₃₉	C₄×D₄	1	8	yes	—
152	C₂×C₄×C₁₃₉	#121	1	4	yes	—
153	C₂×C₄×C₁₃₉	#124	1	4	yes	—
154	C₂×C₄×C₁₃₉	#127	1	4	yes	—
155	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
157	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
159	C₈×C₁₃₉	—	4	4	no	—
160	C₂²×C₁₃₉	—	2	4	no	—
161	C₂²×C₁₃₉	—	2	8	no	—
162	C₂²×C₁₃₉	—	4	8	no	—
163	C₂²×C₁₃₉	—	4	4	no	—
164	C₂²×C₁₃₉	—	8	16	no	—
165	C₂²×C₁₃₉	—	8	8	no	—
166	C₂²×C₁₃₉	#390	1	4	yes	—
167	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₁₃₉	C₂×#121	1	2	yes	—
169	C₂²×C₁₃₉	#575	1	4	yes	—
170	C₄×C₁₃₉	—	2	4	no	—
171	C₄×C₁₃₉	—	2	4	no	—
172	C₄×C₁₃₉	—	4	8	no	—
173	C₄×C₁₃₉	—	4	4	no	—
174	C₄×C₁₃₉	#390	1	4	yes	—
175	C₄×C₁₃₉	C₂×C₄×D₄	1	2	yes	—
176	C₄×C₁₃₉	C₂×#124	1	1	yes	characteristic
177	C₄×C₁₃₉	C₂×#127	1	1	yes	characteristic
178	C₂×C₁₃₉	—	2	4	no	—
179	C₂×C₁₃₉	—	8	4	no	—
180	C₂×C₁₃₉	C₂×#390	1	1	yes	characteristic
181	C₂×C₁₃₉	#2896	1	2	yes	—
182	C₂×C₁₃₉	#3040	1	4	yes	—
183	#21261	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₁₃₉	#21261	1	1	yes	characteristic, direct product factor, Sylow
185	C₂²×#124	C₂×C₁₃₉	1	1	yes	characteristic
186	C₂×#423	C₂×C₁₃₉	1	1	yes	characteristic, complemented
187	C₂×#419	C₂×C₁₃₉	1	2	yes	complemented
188	C₂×#418	C₂×C₁₃₉	1	2	yes	—
189	C₄×#117	C₂×C₁₃₉	1	1	yes	characteristic, complemented
190	#1983	C₂×C₁₃₉	1	8	yes	complemented
191	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
192	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
193	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
194	C₂×#124	—	2	1	no	—
195	C₂×#124	—	2	1	no	—
196	C₂×#124	—	2	4	no	—
197	C₂×#124	C₄×C₁₃₉	1	8	yes	complemented
198	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
199	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
200	C₂²×C₂²⋊C₄	—	2	2	no	—
201	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
202	#423	—	2	4	no	—
203	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	4	yes	complemented
204	#419	—	2	8	no	—
205	#418	—	2	8	no	—
206	C₂×#103	C₂²×C₁₃₉	1	8	yes	complemented
207	C₂×#102	C₂²×C₁₃₉	1	8	yes	—
208	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
209	C₄×C₂²⋊C₄	—	2	2	no	—
210	#376	—	2	1	no	—
211	C₄³	—	2	1	no	—
212	C₂⁵	—	2	1	no	—
213	C₂²×Q₈	—	2	2	no	—
214	C₂²×Q₈	—	2	1	no	—
215	C₂²×Q₈	—	2	4	no	—
216	C₂²×Q₈	—	2	4	no	—
217	C₂²×Q₈	C₂×C₄×C₁₃₉	1	4	yes	—
218	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
219	C₂²×D₄	—	2	4	no	—
220	C₂²×D₄	—	2	1	no	—
221	C₂²×D₄	—	2	2	no	—
222	C₂²×D₄	—	2	4	no	—
223	C₂²×D₄	C₂×C₄×C₁₃₉	1	4	yes	—
224	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
225	C₂³×C₄	—	2	1	no	—
226	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
227	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
228	C₂×M₁₆	—	2	4	no	—
229	C₂×M₁₆	—	2	4	no	—
230	C₂×M₁₆	—	2	4	no	—
231	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
232	#124	—	2	8	no	—
233	#124	—	2	8	no	—
234	#124	—	2	8	no	—
235	#124	C₂×C₄×C₁₃₉	1	16	yes	—
236	#117	—	2	4	no	—
237	#117	D₄×C₁₃₉	1	8	yes	—
238	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
239	C₂×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₂²⋊C₄	—	2	16	no	—
241	C₂×C₂²⋊C₄	—	2	4	no	—
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	—	2	4	no	—
245	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
246	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
247	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
248	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
249	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
250	C₄⋊C₈	—	2	8	no	—
251	#103	—	2	16	no	—
252	#102	—	2	16	no	—
253	#95	—	2	4	no	—
254	C₂⁴	—	2	4	no	—
255	C₂⁴	—	2	2	no	—
256	C₂⁴	—	4	8	no	—
257	C₂⁴	—	4	4	no	—
258	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
259	C₂×Q₈	—	2	4	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	—	2	16	no	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	4	4	no	—
265	C₂×Q₈	—	4	4	no	—
266	C₂×Q₈	—	4	4	no	—
267	C₂×Q₈	C₂²×C₄×C₁₃₉	1	4	yes	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	2	16	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	4	4	no	—
274	C₂×D₄	—	4	4	no	—
275	C₂×D₄	—	4	4	no	—
276	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	4	4	no	—
282	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	8	yes	—
283	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
289	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
290	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
291	M₁₆	—	4	8	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	4	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
297	C₂²⋊C₄	—	2	8	no	—
298	C₂²⋊C₄	—	2	16	no	—
299	C₂²⋊C₄	—	2	16	no	—
300	C₄²	—	2	8	no	—
301	C₄²	—	4	8	no	—
302	C₄²	C₂²⋊C₄×C₁₃₉	1	4	yes	—
303	C₄²	C₂²⋊C₄×C₁₃₉	1	4	yes	—
304	C₄²	C₂²×C₄×C₁₃₉	1	4	yes	—
305	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
306	C₂³	—	2	4	no	—
307	C₂³	—	2	4	no	—
308	C₂³	—	4	16	no	—
309	C₂³	—	4	4	no	—
310	C₂³	—	4	8	no	—
311	C₂³	—	4	8	no	—
312	C₂³	—	8	16	no	—
313	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
314	C₂³	#121×C₁₃₉	1	4	yes	—
315	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
316	Q₈	—	2	8	no	—
317	Q₈	—	4	2	no	—
318	Q₈	—	4	2	no	—
319	Q₈	—	4	8	no	—
320	D₄	—	2	8	no	—
321	D₄	—	4	2	no	—
322	D₄	—	4	2	no	—
323	D₄	—	4	8	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	4	8	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	8	no	—
331	C₂×C₄	—	4	8	no	—
332	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
333	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	4	yes	—
334	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
335	C₂×C₄	C₄×D₄×C₁₃₉	1	8	yes	—
336	C₂×C₄	#121×C₁₃₉	1	4	yes	—
337	C₂×C₄	#124×C₁₃₉	1	4	yes	—
338	C₂×C₄	#127×C₁₃₉	1	4	yes	—
339	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
341	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
342	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
343	C₈	—	4	4	no	—
344	C₂²	—	2	8	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	8	no	—
348	C₂²	—	8	16	no	—
349	C₂²	—	8	8	no	—
350	C₂²	#390×C₁₃₉	1	4	yes	—
351	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
352	C₂²	C₂×#121×C₁₃₉	1	2	yes	—
353	C₂²	#575×C₁₃₉	1	4	yes	—
354	C₄	—	2	4	no	—
355	C₄	—	2	4	no	—
356	C₄	—	4	8	no	—
357	C₄	—	4	4	no	—
358	C₄	#390×C₁₃₉	1	4	yes	—
359	C₄	C₂×C₄×D₄×C₁₃₉	1	2	yes	—
360	C₄	C₂×#124×C₁₃₉	1	1	yes	characteristic
361	C₄	C₂×#127×C₁₃₉	1	1	yes	characteristic
362	C₂	—	2	4	no	—
363	C₂	—	8	4	no	—
364	C₂	C₂×#390×C₁₃₉	1	1	yes	characteristic
365	C₂	#2896×C₁₃₉	1	2	yes	—
366	C₂	#3040×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×#423×C₁₃₉	C₂	semidirect
3. C₂×#419×C₁₃₉	C₂	semidirect
5. C₄×#117×C₁₃₉	C₂	semidirect
6. #1983×C₁₃₉	C₂	semidirect
13. C₂×#124×C₁₃₉	C₄	semidirect
19. C₂×C₄⋊C₈×C₁₃₉	C₂²	semidirect
22. C₂×#103×C₁₃₉	C₂²	semidirect
24. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
183. #21261	C₁₃₉	direct (N × H)
184. C₁₃₉	#21261	direct (N × H)
186. C₂×#423	C₂×C₁₃₉	semidirect
187. C₂×#419	C₂×C₁₃₉	semidirect
189. C₄×#117	C₂×C₁₃₉	semidirect
190. #1983	C₂×C₁₃₉	semidirect
197. C₂×#124	C₄×C₁₃₉	semidirect
203. C₂×C₄⋊C₈	C₂²×C₁₃₉	semidirect
206. C₂×#103	C₂²×C₁₃₉	semidirect
208. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#124×C₁₃₉	2
C₂×#423×C₁₃₉	2
C₂×#419×C₁₃₉	2
C₂×#418×C₁₃₉	2
C₄×#117×C₁₃₉	2
#1983×C₁₃₉	2
#21261	139

Subgroups — C139×#21261 #48015857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#21261 #48015857